Magnetic fields • Magnetic field of a planet (Earth) • Dipole • Higher orders • Short period variations • Secular variations • Polar drift • Paleomagnetism • Magnetic fields of other planets • Remnant fields Reference: Physics of the Earth, F. D. Stacey & P. M. Davis, Cambridge University Press, 2008
Magnetic fields. Magnetic field of a planet (Earth) Dipole Higher orders Short period variations Secular variations Polar drift Paleomagnetism Magnetic fields of other planets Remnant fields Reference: Physics of the Earth, F. D. Stacey & P. M. Davis, Cambridge University Press, 2008. - PowerPoint PPT Presentation
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Magnetic fields
• Magnetic field of a planet (Earth)• Dipole• Higher orders• Short period variations• Secular variations• Polar drift• Paleomagnetism• Magnetic fields of other planets• Remnant fields
Reference:Physics of the Earth, F. D. Stacey & P. M. Davis, Cambridge
University Press, 2008
Magnetic fields of a planet
• Many planets/moons have a magnetic field
• In first order it is a dipolar field, higher orders exist
• The source is inside the planet• The magnetic field axes do not
necessarily coincide with the rotation axis of the planet
• The dipole centre can be offset from the planetary centre
• The magnetic field is variable on any timescale [ms – Myears]
• The pole direction can reverse• A planetary magnetic field can
vanish if the driving mechanism is diminished (e.g. Mars)
Field intensity of the Earth magnetic field
Image: NOAA/NGDC & CIRES
Field declination
Field inclination
Historical
• Magnetic properties of lodestones were recognised already by ~600BC
• It was attributed to a effluvium in Greece or qi in China which was essentially a life energy
• Initially only the horizontal orientation (declination) was used for navigation
• The magnetic declination i.e. the deviation of the magnetic poles from the geographic poles was recognised and applied in navigation maps in the 16th century
• The inclination of the magnetic field was confirmed in the 16th century but still was disputed later on
• At 1600 the magnetic field of spherical lodestones was described as a quadrupole field (W. Gilbert, De Magnete, 1600, ISBN-10: 048626761X )
• Secular variations were reported from the 15 - 16th century on• The magnetic field as an internal field was confirmed not before the
early 20th century and was contested by e.g. Einstein until 1940
Left: HM 46. PORTOLAN ATLAS and NAUTICAL ALMANAC. France, 1543Right: De Magnete 1628 Edition
Field creation mechanism
• A planetary magnetic field is assumed to be created by electric currents in a liquid electrical conducting part of the outer core.
• The magnetic induction equation describes the field creation by a moving fluid
• ηm is the magnetic diffusivity,• σ electrical conductivity,• μ magnetic permeabiltiy,• v fluid velocity which is sustained by convection• When v → 0 the dipole would vanish within some tens of thousands
years
1
2
BvBtB
m
Image: USGS
Field propagation & attenuation
• Field generated in core < Re/2• Small scale features are hidden
because of distance to surface and magnetisation in crust
• Electrical conductivity in mantle is contributing to field attenuation– (Gaillard et al. Carbonatite Melts
and Electrical Conductivity in the Asthenosphere. Science, 2008; 322 (5906): 1363 DOI: 10.1126/science.1164446)
• Unmaintained electric currents in the core would decay due to ohmic dissipation within 104 years
Electrical conductivity map of earth mantle. Image: Anna Kelbert, Oregon State University 2009
Best fitting dipole
• A planetary magnetic field can (mostly) be represented in first order by a dipole field with the magnetic moment m
• The magnetic potential Vm of the best fitting dipole is
222 Am10768.7
Earthm
iAm
Äquator5
30
0
30
0
300
0
23
ra Gauss3004.0T10004.34
cos24
sin4
4cos
4
amB
rm
rVBr
rmV
rB
gradVBr
mrrmV
Earth
m
m
m
m
Non dipole elements
• About 20% of earths magnetic field are contributions from higher pole orders.
• Spherical harmonic coefficients for a internal field can be found using:
• The coefficients g and h are given in nanoTesla (nT) and can be derived from satellite measurements
• The angle η between the magnetic and geographic axes is 10.26°
cossincos1 0
1
0Phg m
ll
l
m
m
l
m
l
l
m lmmraaV
26.10192.0tan
01
211
211
211
211
2010
ghg
hggB
Short period variations
• Short period variations are mostly induced by external events– Solar Flares– Magnetic storms in the
solar wind
• -> See next unit on magnetospheres and solar planetary interactions
Secular variations
• Changing patterns in the core motion drive slow variations in the magnetic field (> 1 year)
• Most extra-terrestrial effects are short periodic
• Changes are not uniform on a global scale
• Currently we observe a field drift of about 0.2°/year for the higher harmonics
• The total field strength over the last centuries has decreased by ~6.3%/century
• Over geological timescales pole reversals have been found
Paleomagnetism
• Iron rich lava can trap the current local magnetic field direction while cooling
• The paleomagnetic field can be reconstructed from bore stems
Polar drift
• Over geologic timescales the position of the magnetic poles can change
• Thus far about 170 polar reversals have been found
• Today the north pole is moving towards Siberia with an average speed of 10 km/year
• Recently the speed has increased to ~40 km/year
Magnetic fields of other planets
Magnetic fields of other planets
Planet Dipole Moment [Am2] Dynamo Surface Field [nT]
Mercury 5x1019 probable 457
Venus <4x1018 No <2.5
Earth 8x1022 Yes 41455
Mars ~1x1018 No 3.5
Jupiter 1.6x1027 Yes 650000
Saturn 4.7x1025 Yes 32850
Uranus 3.8x1024 Yes 32170
Neptune 2.0x1024 Yes 18560
Remnant Magnetic Field of Mars
• Due to the lack of plate tectonics i.e. large internal convection the dynamo process on Mars has stopped
• The remnant magnetic field is very weak and consists mostly of multi-pole contributions
• The paleomagnetic field was observed from orbit by the MGS orbiter in 1999
Image: MGS/NASA
Magnetic field of the Moon
Induced magnetic field
• The solar wind can produce an induced magnetic field around planets/moons with an atmosphere or rather an ionosphere
• E.g. Venus and Titan when outside the Saturn magnetosphere